The Benefits Of A 100-Shot Group
To see how illustrative a small sampling might be, I decided to fire 100 rounds of the same ammo, out of the same rifle, during identical shooting and atmospheric conditions. My thinking was 100 carefully fired and recorded shots should provide a more practical picture of performance. The results changed the way I look at performance testing results, and might explain some of the misses we sometimes experience.
[ … ]
If we accept this 100-shot accuracy test as being representative, it’s clear simply firing and chronographing a couple three- or five-shot groups is not illustrative of how any rifle/load combination will perform over time. If you want to know what you can really expect from your rifle, every time you pull the trigger on a certain load, you need to evaluate more than one box of ammo.
In this article he deals only with those pseudo-random variables like velocity due to differences in loading, bullet weight, etc. While it is well beyond the scope of this post, there are also things like stochastic vibration propagation along grain boundaries and crystalline structures of the gun barrel, which gets very complicated. That subject cannot be given justice here.
When you fire a 3-shot group and claim that the gun shoots “__” MOA, or a 5-shot group and that the gun is capable of “__” MOA, that’s only marginally useful. That data doesn’t meet the Central Limit Theorem (CLT) for convergence and presence of at least three moments (a mean, fractional standard deviation of < 5% and a Variance of the Variance that is acceptable to an analyst).
But 3-shot and 5-shot groups is all you’ll ever see from a gun manufacturer. Just realize that this is essentially meaningless and much more is needed to yield a standard distribution with proper variance.

